In recent years, as a large scale integrated circuit (LSI) is having higher integration and larger capacity, circuit line width required for semiconductor devices is becoming smaller and smaller. The semiconductor devices are manufactured by forming circuits by exposing and transferring a pattern on a wafer by a reduced projection exposure apparatus which is a so-called stepper using an original image pattern (also called a mask or a reticle, hereinbelow, generically called a mask) in which a circuit pattern is formed.
For manufacture of an LSI whose cost is extremely high, it is essential to improve die yield. One of main factors of deteriorating the yield is a pattern defect in a mask used at the time of exposing and transferring an ultrafine pattern onto a semiconductor wafer. In recent years, as the dimensions of an LSI pattern formed on a semiconductor wafer are becoming smaller, the dimensions of a pattern defect to be detected are also becoming extremely small. Consequently, it requires higher precision of a pattern inspection apparatus for inspecting a defect in a mask used for LSI manufacture.
The pattern defect inspecting method is largely divided into a die to die (DD) comparison inspection and a die to database (DB) comparison inspection. The DD comparison inspection is a method of detecting a defect by comparing measurement data of two dies on a mask (an inspection reference pattern image and a pattern image to be inspected). The DB comparison inspection is a method of detecting a defect by comparing measurement data of a die (data of a pattern image to be inspected) and design data of the die generated from CAD data for LSI designing (data of the inspection reference pattern image).
In the DB comparison inspection, a specimen is placed on a stage of a pattern inspection apparatus and is scanned with a light flux when the stage is moved, and an inspection is performed. The specimen is irradiated with the light flux from a light source and an illumination optical system. An image is formed on a sensor by light passed through the specimen or reflected from the specimen via the optical system. The image picked up by the sensor is transmitted as measurement data to a comparison circuit. In the comparison circuit, after positioning of the images, measurement data and design data is compared with each other by using a proper algorithm. When the data do not match, presence of a pattern defect is determined.
In recent years, as a pattern on a mask for lithography is becoming smaller, it becomes necessary to detect a small defect which is hidden by a positional deviation between images to be compared, expansion and contraction of the images, a wave in the image, sensing noise, and the like. Consequently, the inspection reference pattern image and the pattern image to be inspected have to be positioned with high precision. Further, to detect these defects, image correction is important. Therefore, prior to comparison inspection, the inspection reference pattern image and the pattern image to be inspected are aligned. After that, image corrections are performed in order such as correction of expansion and contraction of the images (for example, JP-A No. 2000-241136 (KOKAI), correction of a wave in an image, resize correction, noise averaging process, and the like.
However, when such corrections are repeated, an accumulated error is caused, and it causes deterioration in an image. Further, when the inspection reference pattern image and the pattern image to be inspected become excessively closer to each other due to excessive corrections, it becomes difficult to detect a defect. That is, the excessive corrections produce the opposite effect.
JP 3965189 discloses image correction using an input/output prediction model as effective image correction with little image deterioration by unifying an alignment for final fine adjustment from a sub-pixel level and image correction. In the image correction, for example, alignment on the sub-pixel unit basis and image correction are simultaneously realized by using an inspection reference pattern image as input data and using a pattern image to be inspected as output data. In this case, a relational expression of a matrix is generated from image data. By solving simultaneous equations, a model parameter (coefficient) is identified. On the basis of a two-dimensional linear prediction model to which the identified model parameter is applied, the inspection reference pattern image is corrected, thereby generating a corrected pattern image.